Question

two functions are given.
$f(x)=\frac{1}{2}x - 3$
$g(x)=\frac{7}{10}x - 6$
what is the solution to $f(x)=g(x)$?
$x = \boxed{}$

Explanation:

Step1: Set \( f(x) = g(x) \)

We have \( f(x)=\frac{1}{2}x - 3 \) and \( g(x)=\frac{7}{10}x - 6 \). Setting them equal gives \(\frac{1}{2}x - 3=\frac{7}{10}x - 6\).

Step2: Eliminate fractions

Multiply every term by 10 (the least common denominator of 2 and 10) to get \( 10\times(\frac{1}{2}x)-10\times3 = 10\times(\frac{7}{10}x)-10\times6 \). Simplifying, we have \( 5x - 30 = 7x - 60 \).

Step3: Solve for \( x \)

Subtract \( 5x \) from both sides: \( - 30 = 2x - 60 \). Then add 60 to both sides: \( 30 = 2x \). Divide both sides by 2: \( x = 15 \).

Answer:

\( 15 \)